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Yayın Exploiting epistemic uncertainty of the deep learning models to generate adversarial samples(Cornell Univ, 2021-02-13) Tuna, Ömer Faruk; Çatak, Ferhat Özgür; Eskil, Mustafa TanerDeep neural network architectures are considered to be robust to random perturbations. Nevertheless, it was shown that they could be severely vulnerable to slight but carefully crafted perturbations of the input, termed as adversarial samples. In recent years, numerous studies have been conducted in this new area called "Adversarial Machine Learning" to devise new adversarial attacks and to defend against these attacks with more robust DNN architectures. However, almost all the research work so far has been concentrated on utilising model loss function to craft adversarial examples or create robust models. This study explores the usage of quantified epistemic uncertainty obtained from Monte-Carlo Dropout Sampling for adversarial attack purposes by which we perturb the input to the areas where the model has not seen before. We proposed new attack ideas based on the epistemic uncertainty of the model. Our results show that our proposed hybrid attack approach increases the attack success rates from 82.59% to 85.40%, 82.86% to 89.92% and 88.06% to 90.03% on MNIST Digit, MNIST Fashion and CIFAR-10 datasets, respectively.Yayın Some remarks on uniform boundary Harnack principles(Cornell Univ, 2021-03-18) Barlow, Martin T.; Karlı, DenizWe prove two versions of a boundary Harnack principle in which the constants do not depend on the domain by using probabilistic methods.Yayın Matched pair analysis of the Vlasov plasma(Cornell Univ, 2021-02-09) Esen, Oğul; Sütlü, SerkanWe present the Hamiltonian (Lie-Poisson) analysis of the Vlasov plasma, and the dynamics of its kinetic moments, from the matched pair decomposition point of view. We express these (Lie-Poisson) systems as couplings of mutually interacting (Lie-Poisson) subdynamics. The mutual interaction is beyond the well-known semi-direct product theory. Accordingly, as the geometric framework of the present discussion, we address the matched pair Lie-Poisson formulation allowing mutual interactions. Moreover, both for the kinetic moments and the Vlasov plasma cases, we observe that one of the constitutive subdynamics is the compressible isentropic fluid flow, and the other is the dynamics of the kinetic moments of order > 2. In this regard, the algebraic/geometric (matched pair) decomposition that we offer, is in perfect harmony with the physical intuition. To complete the discussion, we present a momentum formulation of the Vlasov plasma, along with its matched pair decomposition.Yayın Cohomologies and generalized derivation extensions of n-Lie algebras(Cornell Univ, 2021-04-18) Ateşli, Begüm; Esen, Oğul; Sütlü, SerkanA cohomology theory, associated to a n-Lie algebra and a representation space of it, is introduced. It is observed that this cohomology theory is qualified to encode the generalized derivation extensions, and that it coincides, for n = 3, with the known cohomology of n-Lie algebras. The abelian extensions and infinitesimal deformations of n-Lie algebras, on the other hand, are shown to be characterized by the usual cohomology of n-Lie algebras. Furthermore, the Hochschild-Serre spectral sequence of the Lie algebra cohomology is upgraded to the level of n-Lie algebras, and is applied to the cohomology of generalized derivation extensions.Yayın Tulczyjew's triplet for Lie groups III : higher order dynamics and reductions for iterated bundles(Cornell Univ, 2021-02-23) Esen, Oğul; Gümral, Hasan; Sütlü, SerkanGiven a Lie group G, we elaborate the dynamics on T*T*G and T*T G, which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew symplectic space TT*G, which may be defined by a Lagrangian or a Hamiltonian function. As the trivializations we adapted respect the group structures of the iterated bundles, we exploit all possible subgroup reductions (Poisson, symplectic or both) of higher order dynamics.Yayın Quantum van Est isomorphism(Cornell Univ, 2022-05-07) Kaygun, Atabey; Sütlü, SerkanMotivated by the fact that the Hopf-cyclic (co)homology of the quantized algebras of functions and quantized universal enveloping algebras are the correct analogues of the Lie algebra and Lie group (co)homologies, we hereby construct three van Est type isomorphisms between the Hopf-cyclic (co)homologies of Lie groups and Lie algebras, and their quantum groups and corresponding enveloping algebras, both in h-adic and q-deformation frameworks.Yayın Unsupervised textile defect detection using convolutional neural networks(Cornell Univ, 2023-11-30) Koulali, Imane; Eskil, Mustafa TanerIn this study, we propose a novel motif-based approach for unsupervised textile anomaly detection that combines the benefits of traditional convolutional neural networks with those of an unsupervised learning paradigm. It consists of five main steps: preprocessing, automatic pattern period extraction, patch extraction, features selection and anomaly detection. This proposed approach uses a new dynamic and heuristic method for feature selection which avoids the drawbacks of initialization of the number of filters (neurons) and their weights, and those of the backpropagation mechanism such as the vanishing gradients, which are common practice in the state-of-the-art methods. The design and training of the network are performed in a dynamic and input domain-based manner and, thus, no ad-hoc configurations are required. Before building the model, only the number of layers and the stride are defined. We do not initialize the weights randomly nor do we define the filter size or number of filters as conventionally done in CNN-based approaches. This reduces effort and time spent on hyperparameter initialization and fine-tuning. Only one defect-free sample is required for training and no further labeled data is needed. The trained network is then used to detect anomalies on defective fabric samples. We demonstrate the effectiveness of our approach on the Patterned Fabrics benchmark dataset. Our algorithm yields reliable and competitive results (on recall, precision, accuracy and f1- measure) compared to state-of-the-art unsupervised approaches, in less time, with efficient training in a single epoch and a lower computational cost.Yayın Age of information in practice(Cornell Univ, 2021-06-02) Uysal, Elif; Kaya, Onur; Baghaee, Sajjad; Beytur, Hasan BurhanWhile age of Information (AoI) has gained importance as a metric characterizing the fresh-ness of information in information-update systems and time-critical applications, most previous studies on AoI have been theoretical. In this chapter, we compile a set of recent works reporting API measurements in real-life networks and experimental testbeds, and investigating practical issues such as synchronization, the role of various transport layer protocols, congestion control mechanisms, application of machine learning for adaptation to network conditions, and device related bottlenecks such as limited processing power.Yayın Setting standards in Turkish NLP: TR-MMLU for large language model evaluation(Cornell Univ, 2025-01-04) Bayram, M. Ali; Fincan, Ali Arda; Gümüş, Ahmet Semih; Diri, Banu; Yıldırım, Savaş; Aytaş, ÖnerLanguage models have made remarkable advancements in understanding and generating human language, achieving notable success across a wide array of applications. However, evaluating these models remains a significant challenge, particularly for resource-limited languages such as Turkish. To address this gap, we introduce the Turkish MMLU (TR-MMLU) benchmark, a comprehensive evaluation framework designed to assess the linguistic and conceptual capabilities of large language models (LLMs) in Turkish. TR-MMLU is constructed from a carefully curated dataset comprising 6,200 multiple-choice questions across 62 sections, selected from a pool of 280,000 questions spanning 67 disciplines and over 800 topics within the Turkish education system. This benchmark provides a transparent, reproducible, and culturally relevant tool for evaluating model performance. It serves as a standard framework for Turkish NLP research, enabling detailed analyses of LLMs’ capabilities in processing Turkish text and fostering the development of more robust and accurate language models. In this study, we evaluate state-of-the-art LLMs on TR-MMLU, providing insights into their strengths and limitations for Turkish-specific tasks. Our findings reveal critical challenges, such as the impact of tokenization and fine-tuning strategies, and highlight areas for improvement in model design. By setting a new standard for evaluating Turkish language models, TR-MMLU aims to inspire future innovations and support the advancement of Turkish NLP research.Yayın Higher analogues of discrete topological complexity(Cornell Univ, 2024-04-16) Alabay, Hilal; Borat, Ayşe; Cihangirli, Esra; Erdal, Esma DiricanIn this paper, we introduce the n−th discrete topological complexity and study its properties such as its relation with simplicial LusternikSchnirelmann category and how the higher dimensions of discrete topological complexity relate with each other. Moreover, we find a lower bound of n−discrete topological complexity which is given by the n−th usual topological complexity of the geometric realisation of that complex. Furthermore, we give an example for the strict case of that lower bound.
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